On the Use of Duality and Geometry in Layouts for ATM Networks

Abstract. We show how duality properties and geometric considerations are used in studies related to virtual path layouts of ATM networks. We concentrate on the one-to-many problem for a chain network, in which one constructs a set of paths, that enable connecting one vertex with all others in the network. We consider the parameters of load (the maximum number of paths that go through any single edge) and hop count (the maximum number of paths traversed by any single message). Optimal results are known for the cases where the routes are shortest paths and for the general case of unrestricted paths. These solutions are symmetric with respect to the two parameters of load and hop count, and thus suggest duality between these two. We discuss these dualities from various points of view. The trivial ones follow from corresponding recurrence relations and lattice paths. We then study the duality properties using trees; in the case of shortest paths layouts we use binary trees, and in the gen...

• Type: Conference
• Year: 2000
• Where: MFCS
• Authors: Shmuel Zaks
• Keywords: Duality Properties, MFCS 2000, Paths Case, Shortest Paths, Theoretical Computer Science